### Abstract

Let R be a prime ring and set [x, y]_{1} = [x, y] = xy - yx for x, y ∈ R and inductively [x, y]_{k} = [[x, y]_{k-1}, y] for k > 1. We apply the theory of generalized polynomial identities with automorphisms and skew derivations to obtain the following result: If δ is a nonzero σ-derivation of R and L is a noncommutative Lie ideal of R so that [δ(x), x]_{k} = 0 for all x ∈ L, where k is a fixed positive integer, then charR = 2 and for some field F. This result generalizes the case of derivations by Lanski and also the case of automorphisms by Mayne.

Original language | English |
---|---|

Pages (from-to) | 259-270 |

Number of pages | 12 |

Journal | Monatshefte fur Mathematik |

Volume | 158 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 Jan 1 |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Fingerprint Dive into the research topics of 'An engel condition with skew derivations'. Together they form a unique fingerprint.

## Cite this

Chou, M. C., & Liu, C. K. (2009). An engel condition with skew derivations.

*Monatshefte fur Mathematik*,*158*(3), 259-270. https://doi.org/10.1007/s00605-008-0043-5